Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
5490 conjugacy classes of subgroups; only the 2878 normal subgroups are shown.
This group has 5490 conjugacy classes of subgroups — too many to draw. Only its 2878 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22582680 | C3 | semidirect |
| 2. #22582679 | C3 | semidirect |
| 3. #22582678 | C3 | semidirect |
| 4. #22582677 | C3 | semidirect |
| 6. C3×#15688531 | C3 | semidirect |
| 7. #737×C37⋊C3 | C3 | semidirect |
| 8. C3×C37×#737 | C3 | semidirect |
| 9. #15688532 | C32 | semidirect |
| 10. #15688531 | C32 | semidirect |
| 11. #15688531 | C32 | semidirect |
| 12. #15688531 | C32 | semidirect |
| 13. #15688531 | C32 | semidirect |
| 14. #15688531 | C32 | semidirect |
| 15. #15688530 | C32 | semidirect |
| 16. C3×#11758608 | C32 | semidirect |
| 17. C3×#11758605 | C32 | semidirect |
| 18. C3×#11758606 | C32 | semidirect |
| 19. 3−1+2×C37⋊C3 | C32 | semidirect |
| 22. C3×C9×C37⋊C3 | C32 | semidirect |
| 23. C37×#737 | C32 | semidirect |
| 24. C37×#737 | C32 | semidirect |
| 25. C37×#737 | C32 | semidirect |
| 26. C3×3−1+2×C37 | C32 | semidirect |
| 28. C32×C9×C37 | C32 | semidirect |
| 67. C3×#737 | C37⋊C3 | semidirect |
| 79. #737 | C3×C37⋊C3 | semidirect |
| 80. #737 | C3×C37⋊C3 | semidirect |
| 81. #737 | C3×C37⋊C3 | semidirect |
| 86. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 91. C32×C9 | C3×C37⋊C3 | semidirect |
| 92. C37 | #10624943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582680 | 3 |
| #22582679 | 3 |
| #22582678 | 3 |
| #22582677 | 3 |
| C37⋊H(5,𝔽3) | 3 |
| C3×#15688531 | 3 |
| #737×C37⋊C3 | 3 |
| C3×C37×#737 | 3 |
| #10624943 | 37 |